Answer to Problem 57

To integrate



Equation 92

write



Equation 93



Equation 94

then



Equation 95



Equation 96

Integration with respect to and gives



Equation 97

Substitute to get



Equation 98

Applying the boundary condition , we find :



Equation 99

Now use this equation to substitute for in (*).



Equation 100



Equation 101

This gives



Equation 102

Let . Then (6.4) simplifies to



Equation 103